Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊#66772 |
| unambiguous semidirect product | C3⋊(C5×#66772) |
| Fitting, socle, Hall | C3×C52×C17 ⋊ C4 |
| derived | C3×C5×C17 ⋊ C4×C5 |
| Hall | C52×C17 ⋊ Dic3 |
| Hall | C3×C52 ⋊ #595 |
| Hall | C3×C17 ⋊ C5×Dic5 |
| Sylow | C52 ⋊ C3⋊#595 |
| Sylow | C17 ⋊ C5×Dic15 |
| Sylow | C3 ⋊ C5×#66772 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊#66772 |
| commutator, hypocenter | C3×C5×C17 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C17 | C4 |
| LCS | G ▷ C3×C5×C17 | |
| UCS | C1 ◁ C5 | |
64 conjugacy classes of subgroups.
390 conjugacy classes — view the full character table.
| maximal subgroup of | #29505749, C5×C9⋊#66772, C3⋊#19099756, … |
| maximal normal subgroup of | C3×C5×C3⋊#66772, C5×C7×C3⋊#66772 |
| maximal quotient of | C5×C9⋊#66772, C3×C5×C3⋊#66772, C5×C3⋊(C3⋊#66772), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 105);